This issue came up indirectly in the 9th grade Government classes I teach today [some of my students are quite bright]. Among the issues we were reviewing for the quiz tomorrow are the various ways one becomes a citizen.
One is considered a citizen by birth by being born on U.S. soil [ius soli] provided that at the time one is born one is subject to U.S. law [14th Amendment] - the exemption would obviously being born as a member of the household of an accredited diplomat, one would not be a U.S. citizen by birth because one is not in that case subject to U.S. lazw (diplomatic immunity).
So imagine the following. If at any point in its history as a U.S. naval base, Guantanamo Bay Naval Station has been the locale for the birth of a child neither of whose parents was at the time a U.S. Citizen and that child subsequently functioned as a natural born citizen -- voting without going through naturalization, for example --- that would have established the legal precedent that the territory of Gitmo is subject to U.S. jurisdiction. If so, then by this precedent and by extension the prisoners we are holding at Camp X-ray would also come under the jurisdiction of the U.S. Civil Court system.
I do not know if there is such a precedent. If anyone does, perhaps passing this information on to those lawyers attempting to act on behalf of the prisoners might be useful? [I'm not a lawyer, I don't play one on TV, I just each government].